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Various numerical methods for modeling wave propagation are presented in the literature. These models are specified by the inclusion of nonlinearity and dispersion. The nonlinear Shallow Water Equations (SWEs) and Boussinesq equations are two main sets for wave-based problems. Lattice Boltzmann Method (LBM) is a productive method for solving various CFD problems like issues in the field of free-surface flow problems, that is derived for SWEs in the literature and solved by various numerical methods. In the present study, the 1-D extended Boussinesq system of equations is used as the base equation. Then, this system of equation is converted to Lattice Boltzmann form for the first time. The meshless Element-Free Galerkin (EFG) form of the converted equation is derived and used as the numerical method for wave propagation problems to cover the discontinuous nature of the wave problems. The new orthogonal moving least approximations is defined for the EFG method to avoid singularity in the simulations. Various examples are simulated by the presented numerical model and compared with experimental and other numerical methods. As illustrated in detail in the text, there is high accuracy between the presented results with the experimental and numerical data.

Simulation of 1-D wave propagation by Meshless Lattice Boltzmann method based on Extended Boussinesq equations